The first excited state of three-dimensional isotropic harmonic oscillator (of natural angular frequency wo and mass m) is three-dold degenerate, Use the perturbation inethod to calculate the splitting (to the first order) of this thhrce-fold degenerate state due to a small perturbation of the form bry, where b is a constant. Give the first-order wave functions of the three split levels in terms of the wave functions of the unperturbed three-dimensional harmonic oscillator, given that, for a onc-dimensional lharmonic oscillator, H' <끼피n + 1} (n + 1)h 2mwo
The first excited state of three-dimensional isotropic harmonic oscillator (of natural angular frequency wo and mass m) is three-dold degenerate, Use the perturbation inethod to calculate the splitting (to the first order) of this thhrce-fold degenerate state due to a small perturbation of the form bry, where b is a constant. Give the first-order wave functions of the three split levels in terms of the wave functions of the unperturbed three-dimensional harmonic oscillator, given that, for a onc-dimensional lharmonic oscillator, H' <끼피n + 1} (n + 1)h 2mwo
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Transcribed Image Text:The first excited state of three-dimensional isotropic harmonic oscillator
(of natural angular frequency wo and mass m) is three-dold degenerate,
Use the perturbation inethod to calculate the splitting (to the first order)
of this three-fold degenerate state due to a small perturbation of the form
bry, where b is a constant. Give the first-order wave functions of
the three split levels in terms of the wave functions of the unperturbed
three-dimensional harmonic oscillator, given that, for a onc-dimensional
lharmonic oscillator,
H'
(n|x|n + 1)
(n + 1)h
2mwo
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